class: center, middle, inverse, title-slide # Detecting Nonstationarity ## A step towards precision ### Micah Klein and Nathan Bracken --- # The Big Picture - Predict the location of non stationary in time series - Given a window a window of interest within a series: How likely will the window contain a non stationary component? - What is non stationary? - Data Generating - Strong Stationary - `\(F_{X}(x_{t_{1+\mathcal{T}}}, ..., x_{t_{n+\mathcal{T}}}) = F_{X}(x_{t_{1}}, ..., x_{t_{n}})\)` - `\(F_{X}\)` -> Probability -> From an integral - Why is it interesting? - How random is any stream of data? - We are trying to predict changes in random variable relationship from their aggregate - Panel vs Plain Time Series --- # Data - Food Supply Time series set from 'Our World in Data' <img src="images/series.png" width="2024" /> - Follows a relatively stable trend with some large deviations --- # Methods - We are Predicting probability - Numerical Outcome - Regression - Using linear regression, elasticnet, boosted trees, logistic regression - Outcome -> The probability some interval is non stationary - Predictors -> Interval Size, Series Size, Start, Calorie per capita - Tuning - Hyper parameters - Lambda, Alpha -> Elastic net - Learning Rate (Different Lambda) - Number of Trees - Tree Depth - Training on many series - Testing on a new series - Five fold cross validation (Its the best) --- # Results and conclusion Measurement of success: RMSE for distance of prediction to actual shock - Probability -> an area over a distance - Bias - Location of Prediction too soon or too late - not enough interval sizes - shocks of series occur close together, overestimate PDF of first shock - Variance - Changing the distribution of prediction - Range to large for location of actual outcome - Performance Limitations/Barriers: Colinearity issues